In this section, we formalize the link prediction (LP) problem and the LP decoders.
Typically, many LP models include an encoder that learns the node-level embeddings \(\mathbf {x}_i, i \in \mathcal {V}\) , where \(\mathcal {V}\)  is the set of nodes, and an decoder \(\phi : \mathbb {R}^d \times \mathbb {R}^d \rightarrow \mathbb {R}\)  that combines the node-level embeddings of a pair of nodes: \(\mathbf {x}_i, \mathbf {x}_j\)  into a single score: \(s_{ij}\) .
If \(s_{ij}\)  is higher, the link between nodes \(i\)  and \(j\)  is more likely to exist.
The state-of-the-art models generally use graph neural networks as the encoders [1]}, [2]}, [3]}, [4]}, [5]}.
From here on, we mainly focus on the decoder \(\phi \) .
